LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ dtrmm()

 subroutine dtrmm ( character side, character uplo, character transa, character diag, integer m, integer n, double precision alpha, double precision, dimension(lda,*) a, integer lda, double precision, dimension(ldb,*) b, integer ldb )

DTRMM

Purpose:
``` DTRMM  performs one of the matrix-matrix operations

B := alpha*op( A )*B,   or   B := alpha*B*op( A ),

where  alpha  is a scalar,  B  is an m by n matrix,  A  is a unit, or
non-unit,  upper or lower triangular matrix  and  op( A )  is one  of

op( A ) = A   or   op( A ) = A**T.```
Parameters
 [in] SIDE ``` SIDE is CHARACTER*1 On entry, SIDE specifies whether op( A ) multiplies B from the left or right as follows: SIDE = 'L' or 'l' B := alpha*op( A )*B. SIDE = 'R' or 'r' B := alpha*B*op( A ).``` [in] UPLO ``` UPLO is CHARACTER*1 On entry, UPLO specifies whether the matrix A is an upper or lower triangular matrix as follows: UPLO = 'U' or 'u' A is an upper triangular matrix. UPLO = 'L' or 'l' A is a lower triangular matrix.``` [in] TRANSA ``` TRANSA is CHARACTER*1 On entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication as follows: TRANSA = 'N' or 'n' op( A ) = A. TRANSA = 'T' or 't' op( A ) = A**T. TRANSA = 'C' or 'c' op( A ) = A**T.``` [in] DIAG ``` DIAG is CHARACTER*1 On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular. DIAG = 'N' or 'n' A is not assumed to be unit triangular.``` [in] M ``` M is INTEGER On entry, M specifies the number of rows of B. M must be at least zero.``` [in] N ``` N is INTEGER On entry, N specifies the number of columns of B. N must be at least zero.``` [in] ALPHA ``` ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry.``` [in] A ``` A is DOUBLE PRECISION array, dimension ( LDA, k ), where k is m when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. Before entry with UPLO = 'U' or 'u', the leading k by k upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading k by k lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity.``` [in] LDA ``` LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' then LDA must be at least max( 1, n ).``` [in,out] B ``` B is DOUBLE PRECISION array, dimension ( LDB, N ) Before entry, the leading m by n part of the array B must contain the matrix B, and on exit is overwritten by the transformed matrix.``` [in] LDB ``` LDB is INTEGER On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ).```
Further Details:
```  Level 3 Blas routine.

-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.```

Definition at line 176 of file dtrmm.f.

177*
178* -- Reference BLAS level3 routine --
179* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
180* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
181*
182* .. Scalar Arguments ..
183 DOUBLE PRECISION ALPHA
184 INTEGER LDA,LDB,M,N
185 CHARACTER DIAG,SIDE,TRANSA,UPLO
186* ..
187* .. Array Arguments ..
188 DOUBLE PRECISION A(LDA,*),B(LDB,*)
189* ..
190*
191* =====================================================================
192*
193* .. External Functions ..
194 LOGICAL LSAME
195 EXTERNAL lsame
196* ..
197* .. External Subroutines ..
198 EXTERNAL xerbla
199* ..
200* .. Intrinsic Functions ..
201 INTRINSIC max
202* ..
203* .. Local Scalars ..
204 DOUBLE PRECISION TEMP
205 INTEGER I,INFO,J,K,NROWA
206 LOGICAL LSIDE,NOUNIT,UPPER
207* ..
208* .. Parameters ..
209 DOUBLE PRECISION ONE,ZERO
210 parameter(one=1.0d+0,zero=0.0d+0)
211* ..
212*
213* Test the input parameters.
214*
215 lside = lsame(side,'L')
216 IF (lside) THEN
217 nrowa = m
218 ELSE
219 nrowa = n
220 END IF
221 nounit = lsame(diag,'N')
222 upper = lsame(uplo,'U')
223*
224 info = 0
225 IF ((.NOT.lside) .AND. (.NOT.lsame(side,'R'))) THEN
226 info = 1
227 ELSE IF ((.NOT.upper) .AND. (.NOT.lsame(uplo,'L'))) THEN
228 info = 2
229 ELSE IF ((.NOT.lsame(transa,'N')) .AND.
230 + (.NOT.lsame(transa,'T')) .AND.
231 + (.NOT.lsame(transa,'C'))) THEN
232 info = 3
233 ELSE IF ((.NOT.lsame(diag,'U')) .AND.
234 + (.NOT.lsame(diag,'N'))) THEN
235 info = 4
236 ELSE IF (m.LT.0) THEN
237 info = 5
238 ELSE IF (n.LT.0) THEN
239 info = 6
240 ELSE IF (lda.LT.max(1,nrowa)) THEN
241 info = 9
242 ELSE IF (ldb.LT.max(1,m)) THEN
243 info = 11
244 END IF
245 IF (info.NE.0) THEN
246 CALL xerbla('DTRMM ',info)
247 RETURN
248 END IF
249*
250* Quick return if possible.
251*
252 IF (m.EQ.0 .OR. n.EQ.0) RETURN
253*
254* And when alpha.eq.zero.
255*
256 IF (alpha.EQ.zero) THEN
257 DO 20 j = 1,n
258 DO 10 i = 1,m
259 b(i,j) = zero
260 10 CONTINUE
261 20 CONTINUE
262 RETURN
263 END IF
264*
265* Start the operations.
266*
267 IF (lside) THEN
268 IF (lsame(transa,'N')) THEN
269*
270* Form B := alpha*A*B.
271*
272 IF (upper) THEN
273 DO 50 j = 1,n
274 DO 40 k = 1,m
275 IF (b(k,j).NE.zero) THEN
276 temp = alpha*b(k,j)
277 DO 30 i = 1,k - 1
278 b(i,j) = b(i,j) + temp*a(i,k)
279 30 CONTINUE
280 IF (nounit) temp = temp*a(k,k)
281 b(k,j) = temp
282 END IF
283 40 CONTINUE
284 50 CONTINUE
285 ELSE
286 DO 80 j = 1,n
287 DO 70 k = m,1,-1
288 IF (b(k,j).NE.zero) THEN
289 temp = alpha*b(k,j)
290 b(k,j) = temp
291 IF (nounit) b(k,j) = b(k,j)*a(k,k)
292 DO 60 i = k + 1,m
293 b(i,j) = b(i,j) + temp*a(i,k)
294 60 CONTINUE
295 END IF
296 70 CONTINUE
297 80 CONTINUE
298 END IF
299 ELSE
300*
301* Form B := alpha*A**T*B.
302*
303 IF (upper) THEN
304 DO 110 j = 1,n
305 DO 100 i = m,1,-1
306 temp = b(i,j)
307 IF (nounit) temp = temp*a(i,i)
308 DO 90 k = 1,i - 1
309 temp = temp + a(k,i)*b(k,j)
310 90 CONTINUE
311 b(i,j) = alpha*temp
312 100 CONTINUE
313 110 CONTINUE
314 ELSE
315 DO 140 j = 1,n
316 DO 130 i = 1,m
317 temp = b(i,j)
318 IF (nounit) temp = temp*a(i,i)
319 DO 120 k = i + 1,m
320 temp = temp + a(k,i)*b(k,j)
321 120 CONTINUE
322 b(i,j) = alpha*temp
323 130 CONTINUE
324 140 CONTINUE
325 END IF
326 END IF
327 ELSE
328 IF (lsame(transa,'N')) THEN
329*
330* Form B := alpha*B*A.
331*
332 IF (upper) THEN
333 DO 180 j = n,1,-1
334 temp = alpha
335 IF (nounit) temp = temp*a(j,j)
336 DO 150 i = 1,m
337 b(i,j) = temp*b(i,j)
338 150 CONTINUE
339 DO 170 k = 1,j - 1
340 IF (a(k,j).NE.zero) THEN
341 temp = alpha*a(k,j)
342 DO 160 i = 1,m
343 b(i,j) = b(i,j) + temp*b(i,k)
344 160 CONTINUE
345 END IF
346 170 CONTINUE
347 180 CONTINUE
348 ELSE
349 DO 220 j = 1,n
350 temp = alpha
351 IF (nounit) temp = temp*a(j,j)
352 DO 190 i = 1,m
353 b(i,j) = temp*b(i,j)
354 190 CONTINUE
355 DO 210 k = j + 1,n
356 IF (a(k,j).NE.zero) THEN
357 temp = alpha*a(k,j)
358 DO 200 i = 1,m
359 b(i,j) = b(i,j) + temp*b(i,k)
360 200 CONTINUE
361 END IF
362 210 CONTINUE
363 220 CONTINUE
364 END IF
365 ELSE
366*
367* Form B := alpha*B*A**T.
368*
369 IF (upper) THEN
370 DO 260 k = 1,n
371 DO 240 j = 1,k - 1
372 IF (a(j,k).NE.zero) THEN
373 temp = alpha*a(j,k)
374 DO 230 i = 1,m
375 b(i,j) = b(i,j) + temp*b(i,k)
376 230 CONTINUE
377 END IF
378 240 CONTINUE
379 temp = alpha
380 IF (nounit) temp = temp*a(k,k)
381 IF (temp.NE.one) THEN
382 DO 250 i = 1,m
383 b(i,k) = temp*b(i,k)
384 250 CONTINUE
385 END IF
386 260 CONTINUE
387 ELSE
388 DO 300 k = n,1,-1
389 DO 280 j = k + 1,n
390 IF (a(j,k).NE.zero) THEN
391 temp = alpha*a(j,k)
392 DO 270 i = 1,m
393 b(i,j) = b(i,j) + temp*b(i,k)
394 270 CONTINUE
395 END IF
396 280 CONTINUE
397 temp = alpha
398 IF (nounit) temp = temp*a(k,k)
399 IF (temp.NE.one) THEN
400 DO 290 i = 1,m
401 b(i,k) = temp*b(i,k)
402 290 CONTINUE
403 END IF
404 300 CONTINUE
405 END IF
406 END IF
407 END IF
408*
409 RETURN
410*
411* End of DTRMM
412*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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